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358 LECTunE XXX. 



although there is some reason to suppose that Newtow was before acquainted 

 with the circumstance. 



In 1727, Mr. Bouguer received a prize from the academy of Paris for his 

 essay on the masts of ships, which is said to be ingenious, but by no means 

 practically useful. He was probably tempted by this encouragement to con- 

 tinue his application to similar studies, and about twenty years afterwards 

 he published his valuable essay on the construction and manoeuvres of ships, 

 which appears to have superseded all that had been done before respecting the 

 subjects of his investigation. 



The first researches of Daniel Bernoulli, concerning the properties and mo- 

 tions of fluids, bear also the date of 1727. This justly celebrated man was as 

 happy in his application of mathematies to natural philosophy, as he was 

 ready and skilful in his calculations. The greatest part of his hydraulic 

 theorems are founded on the principle first assumed by Huygens, and called 

 by Leibnitz the law of living or ascending force, which is confessedly only 

 true where there is no loss of velocity, from the imperfection of the elasti. 

 city of the bodies concerned ; for it is only with this limitation, that the mo- 

 tions of any system of bodies are always necessarily such, as to be capable of 

 carrying the common centre of gravity to the height, from which it has des- 

 cended, while the bodies have been acquiring their motions. This law of 

 ascending force is of considerable utility in facilitating the solution of a great 

 variety of problems ; it is certain that mechanical power is always to be es- 

 timated by the product of the mass of a body into the height to which it is 

 capable of ascending; and whatever objections may have been made to the 

 employment of this product as the measure of the force of a body in motion, 

 which is indeed an expression inconsistent with a correct definition of the term 

 force, yet it must be confessed, on the other hand, that some of the best 

 English mathematicians have fallen into material errors for want of paying 

 sufficient attention to the general principle. Bernoulli estimates very justly 

 in this manner the mechanical power of a variety of natural and artificial 

 agents, and among the rest, he examines that of gunpowder ; but from an 

 accidental combination of errors, he states the force of a pound of gunpow- 

 der, as equivalent to the daily labour of 100 men, vvhile in fact the effect 

 which is actually obtained from two tons of powder is no greater than that 



